标题： 标量场在弯曲额外维度中的稳定性 显示英文标题

标题： Stability of Scalar Fields in Warped Extra Dimensions

摘要： 本文建立了一个普遍的理论框架，用于研究具有卷曲额外维度的模型的稳定性，在这些模型中，N个标量场以最小的方式与引力耦合。 我们的分析涵盖了带有边界膜和体标量的Randall-Sundrum模型以及广义的域壁模型。 我们推导出描述此类系统扰动自旋-0谱的薛定谔方程。 这一结果被专门用于使用假超引力生成的势，并且我们证明没有边界膜的模型不存在tachyon模态。 转向零模态的存在性，我们证明了一条准则，该准则将可归一化的零模态数量与标量场的宇称联系起来。 具有确定宇称和仅有奇宇称标量的构造被证明不存在零模态，因此是微扰稳定的。 我们给出了两个具有软墙的域壁模型的具体例子，其中一个允许零模态，另一个不允许。 后者是一个仅使用体标量稳定紧致额外维度的模型的例子，并不需要动力学边界膜。 显示英文摘要

摘要： This work sets up a general theoretical framework to study stability of models with a warped extra dimension where N scalar fields couple minimally to gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk scalars, and general domain-wall models. We derive the Schrodinger equation governing the spin-0 spectrum of perturbations of such a system. This result is specialized to potentials generated using fake supergravity, and we show that models without branes are free of tachyonic modes. Turning to the existence of zero modes, we prove a criterion which relates the number of normalizable zero modes to the parities of the scalar fields. Constructions with definite parity and only odd scalars are shown to be free of zero modes and are hence perturbatively stable. We give two explicit examples of domain-wall models with a soft wall, one which admits a zero mode and one which does not. The latter is an example of a model that stabilizes a compact extra dimension using only bulk scalars and does not require dynamical branes.